The syntactic quotient induces an equivalence relation on M, called the syntactic relation, or syntactic equivalence (induced by S). The right syntactic equivalence is the equivalence relation
Similarly, the left syntactic relation is
The syntactic congruence may be defined as
The definition extends to a congruence defined by a subset S of a general monoid M. A disjunctive set is a subset S such that the syntactic congruence defined by S is the equality relation.
Read more about this topic: Syntactic Monoid
Famous quotes containing the word syntactic:
“The syntactic component of a grammar must specify, for each sentence, a deep structure that determines its semantic interpretation and a surface structure that determines its phonetic interpretation.”
—Noam Chomsky (b. 1928)